Problem: A forest has $800$ pine trees, but a disease is introduced that kills $\dfrac{1}{4}$ of the pine trees in the forest every year. Write a function that gives the number of pine trees remaining $P(t)$ in the forest $t$ years after the disease is introduced. $P(t)=$
If $\dfrac{1}{4}$ of the pine trees are killed each year, that means $\dfrac{3}{4}$ of the pine trees remain each year. So each year, the number of pine trees is multiplied by a factor of $\dfrac34$ (or $0.75$ ). If we start with the initial value, $800$ pine trees, and keep multiplying by $\dfrac34$, this function gives us the number of pine trees $t$ years from now: $P(t)=800\left(\dfrac34\right)^t$